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Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

Regular Vertex

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

The interior angles of an equilateral triangle, square, regular pentagon are 60°, 90°, 108° respectively. The sum of the angles at a point is 360°. So θ = 360 - (60 + 90 + 108) = 102°.

This problem is taken from the UKMT Mathematical Challenges.
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